We conducted a 7-month video-based study in two sixth-grade classrooms focusing on teachers’ metacognitive and heuristic approaches to problem solving. All problem-solving lessons were analysed regarding the extent to which teachers implemented a metacognitive model and addressed a set of eight heuristics. We observed clear differences between both teachers’ instructional approaches. Besides, we examined teachers’ and students’ beliefs about the degree to which metacognitive and heuristic skills were addressed in their classrooms and observed that participants’ beliefs were overall in line with our observations of teachers’ instructional approaches. In addition, we investigated how students’ problem-solving skills developed as a result of teachers’ instructional approaches. A positive relationship between students’ spontaneous application of heuristics to solve non-routine word problems and teachers’ references to these skills in their problem-solving lessons was found. However, this increase in the application of heuristics did not result in students’ better performance on these non-routine word problems.

Here is the abstract of their article:

Teachers in the UK and elsewhere are now expected to foster creativity in young children (NACCCE, 1999; Ofsted, 2003; DfES, 2003; DfES/DCMS, 2006). Creativity, however, is more often associated with the arts than with mathematics. The aim of the study was to explore and document pre-service (in the UK, pre-service teachers are referred to as ‘trainee’ teachers) primary teachers’ conceptions of creativity in mathematics teaching in the UK. A questionnaire probed their conceptions early in their course, and these were supplemented with data from semi-structured interviews. Analysis of the responses indicated that pre-service teachers’ conceptions were narrow, predominantly associated with the use of resources and technology and bound up with the idea of ‘teaching creatively’ rather than ‘teaching for creativity’. Conceptions became less narrow as pre-service teachers were preparing to enter schools as newly qualified, but they still had difficulty in identifying ways of encouraging and assessing creativity in the classroom. This difficulty suggests that conceptions of creativity need to be addressed and developed directly during pre-service education if teachers are to meet the expectations of government as set out in the above documents.

This study investigated Turkish preservice, elementary teachers’ personal mathematics teaching efficacy (PMTE), and science teaching efficacy (PSTE) beliefs at the end of their teacher education program. A majority of the participants believed they were well prepared to teach both elementary mathematics and science, but their PSTE scores were significantly lower than their PMTE scores. However, a significant correlation was found between the PMTE and PSTE scores. No significant gender effect on PMTE and PSTE scores was observed, but unlike the results from other countries, Turkish female preservice elementary teachers were found to have slightly higher PMTE and PSTE scores than their male peers. High school major area was found to be a significant predictor of participants’ PMTE and PSTE scores. Participants with mathematics/science high school majors were found to have significantly higher PMTE and PSTE scores than those with other high school majors.

The purpose of this study was to explore the views of students enrolled at a small United States Midwestern community college toward learning mathematics, and to examine the relationship between student beliefs about mathematic learning and educational experiences with mathematics using Q methodology and open-ended response prompts. Schommer’s (Journal of Educational Psychology, 82, 495–504, 1990) multidimensional theory of personal epistemology provided the structural framework for the development of 36 domain specific Q sort statements. Analysis of the data revealed three distinct but related views of learning mathematic which were labeled Active Learners, Skeptical Learners, and Confident Learners. Chi-square tests of independence revealed no significant differences based on gender. Additionally, there was no evidence for differences based on level of mathematics completed, age, or college hours accumulated. Student’s previous experiences in instructional environments, however, were closely associated with beliefs. Results are discussed in view of the implications for establishing learning environments and considerations in implementing Standards-based curricula in higher education.